In 2008 a work of nonfiction became a New York Times bestseller and went on to sell some 250,000 copies worldwide. It's a familiar story, with one crucial difference: the book was a history of 20th-century classical music. Alex Ross's The Rest is Noise defied every expectation and stereotype to find a reading public beyond the echo-chamber of academic enthusiasts. In 2013, the book will be turned into a year-long festival at London's Southbank Centre, an event artistic director Jude Kelly has described as "probably our most ambitious music project to date", and one that will absorb the London Philharmonic Orchestra's entire concert season and the Southbank's piano and chamber music series. All the UK's major regional orchestras will be involved, together with a lineup of international artists. Beethoven and Brahms are out, and in their place are Britten, Boulez and Berio.

But can Ross's new readers really translate into that most fragile and elusive species – new concert-goers? And how did such a chasm emerge between our living composers and our cultural lives?

"Modern music bores me… I hate much of it, and if possible I will try to avoid hearing it." There can't be many among us, however open-eared, who don't share just a little of composer Hans Eisler's weariness, his suspicion of contemporary music. The riots that famously greeted the Paris premiere of Stravinsky's The Rite of Spring a century ago have long since fallen silent, giving way to a bewildered apathy that has seen modern classical music increasingly sidelined. Composers have retreated from public life into their studies and studios, producing music that, as Debussy put it, "smells of the lamp not the sun".

Bernstein once described the 20th century as the "century of death", and it's a description as true musically as it is historically. Again and again tonality was brutalised and murdered, melody left out to die on a hillside. But still audiences came. The atonal experiments of the Second Viennese School, Strauss's agonised harmonic writhings and even the barely-music of Penderecki, Berio and Stockhausen, all grew directly out of their contexts. In the face of the systematic annihilation of an entire people, the bombing of Hiroshima, how else could composers and listeners respond than by rejecting the reassuring musical certainties and consoling resolutions that had proved a lie.

It was in unpacking these relationships, these interdependencies between history, politics and culture, that Ross's book set itself apart. "I became tremendously excited by the essential drama of the story," he explains, "realising that composers as well as writers and film-makers were major players on the 20th-century stage. For better or worse they were in the thick of it, and that, more than anything, was the story I wanted to tell."

It doesn't get much more in the thick of things than the teenage Hitler making the journey to hear the premiere of Strauss's Salome, or visiting the Wagner festival at Bayreuth each summer. Ross shows us Stalin at the opera, military manoeuvres named after Wagnerian characters, and even the CIA promoting the avant-garde in the wake of the Second World War. The controls and restrictions placed upon composers during this century were unimaginable, as politicians sought to harness the power of the art-form banned from Plato's Republic for taking "the strongest hold" upon the human soul.

Today we can rejoice in our musical freedoms – state control of classical music in the West is as risible as it is unthinkable. So healthy is the neglect of our politicians that with the eyes of the world on the Olympics this summer, classical music barely featured in the ceremonies, and when it did take the spotlight it was only to be lampooned by Rowan Atkinson.

No wonder audiences have deserted it. Compare the diverse and passionate musical responses to the Battle of the Somme to the handful provoked by 9/11, the patriotic and pacifist musical manifestos that grew out of the Second World War to the comparative silence that has greeted conflicts in Iraq and Afghanistan. Earlier this summer, a performance of John Adams's Nixon in China at the BBC Proms played to a sold-out crowd. This unlikely operatic story of the encounter between President Nixon and Chairman Mao offers a model for truly modern opera – opera at once written in a distinctively contemporary idiom and engaging with contemporary political themes.

But works such as Adams's are rare, and still stifled by the weight of historical repertoire. In late 18th-century Leipzig, 84 per cent of the repertoire of the Gewandhaus Orchestra was by living composers. By 1870 it was 24 per cent. Today among Britain's ensembles that number would be lucky to reach the high single figures.

Ross's aim in The Rest is Noise was to address "the cultural predicament of the composer in the 20th century". In transforming a book – and one tellingly that contains no printed musical extracts, relying solely on description – into a concert series, Jude Kelly is confronting the cultural predicament of concert halls in the 21st century. Audiences are rising across the UK – the 2011 Proms played to 94 per cent capacity – but still contemporary music empties seats.

"It's hard for someone to hear a piece of Webern for the first time and just get it," argues Kelly. "If you could, it would be pop music. This festival aims to give people a way in, a determination and curiosity to understand not just to walk away." With this in mind, the festival's concerts will be supplemented by debates, lectures and films. Leading figures from theatre, literature and academia (including Ross himself) will offer their responses to the music, and conventional events will be balanced by more informal listening experiences.

It's an ambitious project, and one whose success surely depends on its tone. Ross's book discusses Stravinsky via Bo Diddley, incorporates the Velvet Underground alongside Varese, and above all is willing to stray anecdotally from the musical path to engage with human relationships and encounters as well as philosophy and politics. It's a difficult and circuitous route to tread within the traditionally restricted world of the concert hall.

If the festival can target those people who have heard of Bach but never made it quite as far as a concert hall, or even more potently those who know their Bach and their Beethoven but run from anything contemporary on principle, then it can surely count itself a success.